Which of the following statements are true?
I. The differential equation of $y = Ae^{x}$ has order 1.
II. Eliminating 2 arbitrary constants gives an equation of order 2.
III. The differential equation of $y = Ae^{x} + Be^{-x}$ is $\frac{d^2y}{dx^2} = y$ .
IV. The differential equation of the lines $y = mx + c$ is $\frac{dy}{dx} = m$ .

All four: I, II, III and IVCorrect answerYour answerI and II onlyCorrect answerYour answerII and III onlyCorrect answerYour answerI, II and III onlyCorrect answerYour answer

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CorrectNot quiteAnswer D

Correct answer: D

I and II: one differentiation per constant. III: $\frac{d^2y}{dx^2} = Ae^{x} + Be^{-x} = y$ .
IV is false: $m$ is one of the constants and must be removed too; the equation is $\frac{d^2y}{dx^2} = 0$ .

Concept: Forming a differential equation from a family of curves
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsForming a differential equation

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